论文标题
多线性疾病的Langevin Dynamics II：重新访问$ p = 2 \，$ spin Dynamics的功能重归其化组
Functional renormalization group for multilinear disordered Langevin dynamics II: Revisiting the $p=2\,$ spin dynamics for Wigner and Wishart ensembles
论文作者
论文摘要
在本文中，我们研究了标准P = 2软旋转动力学模型的稍微修改版本的大型行为，包括四分之一或更高的电位。这种模型的均衡状态对应于有效的田间理论，该理论最近被认为是基于重生组参数中数据科学中信号检测的新型范式。我们考虑了一个类似Langevin的方程式，包括在Wigner或Wishart合奏中留下的疾病术语。然后，我们构建了一个非扰动的重新归一化组形式主义在较大的n个限制中有效，在该限制中，该疾病的特征值分布可以被其分析限制所取代，即Wigner和Marchenko-Pastur定律。这种方法的主要优点之一是，及时的相互作用保持局部性，避免了由于在分区函数级别整合该疾病的方法所产生的非局部性。
In this paper, we investigate the large-time behavior for a slightly modified version of the standard p=2 soft spins dynamics model, including a quartic or higher potential. The equilibrium states of such a model correspond to an effective field theory, which has been recently considered as a novel paradigm for signal detection in data science based on the renormalization group argument. We consider a Langevin-like equation, including a disorder term that leaves in the Wigner or Wishart ensemble. Then we construct a nonperturbative renormalization group formalism valid in the large N limit, where eigenvalues distributions for the disorder can be replaced by their analytic limits, namely the Wigner and Marchenko-Pastur laws. One of the main advantages of this approach is that the interactions remain local in time, avoiding the non-locality arising from the approaches that integrate out the disorder at the partition function level.
